All Algebra II Resources
Example Question #1 : Multiplying And Dividing Logarithms
Rewrite the following logarithmic expression in expanded form (i.e. as a sum and/or difference):
By logarithmic properties:
Combining these three terms gives the correct answer:
Example Question #2 : Multiplying And Dividing Logarithms
Which of the following is equivalent to
Recall that log implies base if not indicated.Then, we break up . Thus, we have .
Our log rules indicate that
So we are really interested in,
Since we are interested in log base , we can solve without a calculator.
We know that , and thus by the definition of log we have that .
Therefore, we have .
Example Question #3 : Multiplying And Dividing Logarithms
Find the value of the Logarithmic Expression.
Use the change of base formula to solve this equation.
Example Question #4 : Multiplying And Dividing Logarithms
Many textbooks use the following convention for logarithms:
What is ?
Remembering the rules for logarithms, we know that .
This tells us that .
This becomes , which is .
Example Question #5 : Multiplying And Dividing Logarithms
What is another way of expressing the following?
Use the rule
Example Question #6 : Multiplying And Dividing Logarithms
Expand this logarithm:
In order to solve this problem you must understand the product property of logarithms and the power property of logarithms . Note that these apply to logs of all bases not just base 10.
log of multiple terms is the log of each individual one:
now use the power property to move the exponent over:
Example Question #7 : Multiplying And Dividing Logarithms
Which of the following is equivalent to ?
We can rewrite the terms of the inner quantity. Change the negative exponent into a fraction.
This means that:
Split up these logarithms by addition.
According to the log rules, the powers can be transferred in front of the logs as coefficients.
The answer is: